## Advances in Operator Theory

- Adv. Oper. Theory
- Volume 2, Number 1 (2017), 1-16.

### Fixed point results for a new mapping related to mean nonexpansive mappings

#### Abstract

Mean nonexpansive mappings were first introduced in 2007 by Goebel and Japón Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given mean nonexpansive mapping of a Banach space, many of the positive results have been derived from knowing that a certain average of some iterates of the mapping is nonexpansive. However, nothing is known about the properties of a mean nonexpansive mapping which has been averaged with the identity. In this paper we prove some fixed point results for a mean nonexpansive mapping which has been composed with a certain average of itself and the identity and we use this study to draw connections to the original mapping.

#### Article information

**Source**

Adv. Oper. Theory, Volume 2, Number 1 (2017), 1-16.

**Dates**

Received: 12 October 2016

Accepted: 20 December 2016

First available in Project Euclid: 4 December 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.aot/1512431510

**Digital Object Identifier**

doi:10.22034/aot.1610.1029

**Mathematical Reviews number (MathSciNet)**

MR3730351

**Zentralblatt MATH identifier**

06692016

**Subjects**

Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

Secondary: 47H14: Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q15]

**Keywords**

mean nonexpansive fixed point approximate fixed point sequence nonexpansive nonlinear operator

#### Citation

Gallagher, Torrey M. Fixed point results for a new mapping related to mean nonexpansive mappings. Adv. Oper. Theory 2 (2017), no. 1, 1--16. doi:10.22034/aot.1610.1029. https://projecteuclid.org/euclid.aot/1512431510